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Algebra 2/Trigonometry Regents Exam 0117
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0117a2
1 What is 510° expressed in radian measure?
1) 2.83
5π
2)
6
17π
3)
6
17π
4)
12
4 Which ordered pair is a solution to the system
below?
x 2 − 4y 2 = 16
1)
2)
3)
4)
2 Four surveys are described below. Which survey
methodology would lead to the least biased
conclusion?
1) One hundred randomly chosen heart surgeons
were polled by telephone about how to get
children to eat healthier foods.
2) A country and western radio station asked one
hundred of its listeners to call a telephone
number and answer a question about rap music.
3) From calls made to one hundred randomly
generated telephone numbers, people replied to
a question about television shows they watch.
4) The first one hundred people who left the
World of Baseball Bookstore replied to a
question about the importance of baseball to
society.
5 Three freshmen, five sophomores, and four juniors
are on the school’s chess team. The coach must
select three students to attend the citywide
tournament. Which expression could be used to
determine how many different groups of three
students can be made from this team?
1) 12 C 3
2) 12 P 3
3) 3 C 1 •5 C 1 •4 C 1
4) 3 P 1 •5 P 1 •4 P 1
6 A survey of high school girls found that the mean
number of text messages sent per day by the girls
was 62, with a standard deviation of 12. If a
normal distribution is assumed, which interval
represents the number of texts sent by 68.2% of the
girls?
1) 38–86
2) 44–80
3) 50–74
4) 56–68
3 When factored completely, x 4 − 13x 2 + 36 is
equivalent to
1) (x 2 − 6)(x 2 − 6)
2)
3)
4)
y = x−4
(0,−4)
(4,0)
(6,2)
(2,−2)
(x 2 − 4)(x 2 − 9)
(x − 2)(x − 2)(x − 3)(x − 3)
(x − 2)(x + 2)(x − 3)(x + 3)
3
2
1
2
7 The expression 9 • 27 is equivalent to
1) 3 2
2)
3)
4)
1
9
2
3
243 2
243
3
4
Algebra 2/Trigonometry Regents Exam 0117
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11 If log 3 (x + 1) − log 3 x = 2, then x equals
9
1) −
8
6
2) −
5
1
3)
8
1
4)
5
1
2
8 The ratio
is equal to
Arc tan1
3
1)
4
3π
2)
4
4
3)
3
4π
4)
3
Arc cos
12 Which relation is not a function?
1) xy = 4
2) y = log 4 x
3) y = 4sinx
9 Which summation will not produce
2 + 4 + 6 + 8 + 10 + 12?
12
1)
∑b
4)
4x 2 − y 2 = 4
b=2
6
2)
13 What is the area of parallelogram ABCD if AB = 4,
AD = 5 3 , and m∠A = 60?
1) 15
2) 30
3) 5 3
∑ 2a
a=1
7
3)
∑ (2d − 2)
d=2
5
4)
4)
2∑ (c + 1)
10 3
c=0
10 The expression
equivalent to
1) 2m 3 − k
2)
3)
4)
1
3

6  3m 2 − k

14 The maximum point on the graph of the equation
y = f(x) is (2,−3). What is the maximum point on
the graph of the equation y = f(x − 4) ?
1) (2,−7)
2) (−2,−3)
3) (6,−7)
4) (6,−3)

3  is

2
2m 3 − 3k 2
2m − k 2
12m − k 6
15 The formula of the nth term of the sequence
3,−6,12,−24,48. . . is
1) a n = −2(3) n
2
2)
a n = 3(−2) n
3)
a n = −2(3) n − 1
4)
a n = 3(−2) n − 1
Algebra 2/Trigonometry Regents Exam 0117
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16 The expression
1)
2)
3)
4)
0
3
3
+
is equivalent to
a −1 1−a
1
and θ terminates in Quadrant II, what
2
is the value of csc θ • cot θ ?
1) −2 3
21 If sin θ =
6
a −1
6
6
1 − a2
2
2)
3)
4)




17 The product of  2 2 + 5i  and  5 2 − 2i  is




1) 30
2) 30 + 21i 2
3)
4)
3
2
−2
2 3
3
22 A circle has a radius of 12 units. For this circle,
which expression incorrectly states the length of
the arc intercepted by the given central angle?
1) angle = 120°
30 + 29i 2
10 + 21i 2
2)
18 Which quadratic equation has roots with a sum of
7
1
and a product of − ?
6
2
2
1) 6x + 7x + 3 = 0
2) 6x 2 + 7x − 3 = 0
3) 6x 2 − 7x − 3 = 0
4) 6x 2 − 7x + 3 = 0
3)
arc length = 8π
angle = 6°
arc length = 72
2
angle = radian
3
arc length = 8
4)
angle =
π
3
radians
arc length = 4π
19 The range of the function f(x) = 3 |x − 4| − 5 is
1) x ≥ 0
2) f(x) ≥ 0
3) x ≥ −5
4) f(x) ≥ −5
23 How many different four-letter arrangements can
be made from the letters in the word “CHAIRS,” if
the same letter may be used only once?
1) 360
2) 420
3) 720
4) 840
20 The graph of the equation y = mx passes through
the point
1) (1,m)
2) (0,m)
3) (m,0)
4) (m,1)
3
Algebra 2/Trigonometry Regents Exam 0117
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27 The graph of f(x) is shown below. Which graph
24 The sets below represent test scores for two
students in Mrs. Silvio’s trigonometry class.
Michelle: {71, 68, 84, 88}
Valerie: {78, 82, 76, 80}
Which statement correctly describes the
relationship between the two students’ test scores?
1) Michelle’s mean test score is greater and her
test scores have a greater interquartile range.
2) Michelle’s population standard deviation is
greater, but her range is smaller.
3) Valerie’s mean test score is greater and her
interquartile range is greater.
4) Valerie’s mean test score is greater, but her
population standard deviation is smaller.
represents f
25 A support wire 20 meters long runs from the top of
a utility pole to a point on the ground 17 meters
from the base of the pole. What is the measure, to
the nearest minute, of the angle formed by the pole
and the wire?
1) 31°47'
2) 31°48'
3) 58°12'
4) 58°13'
26 If f(x) = 3x − 2 and f −1 (x) =
equals
1) x
1
2)
x
3)
4)
−1
(x) ?
1)
2)
x+2
, then f  f −1 (x)
3
3)
 x + 2 

(3x − 2) ÷ 

 3 
 x + 2 

(3x − 2) • 

 3 
4)
28 The number of bacteria that grow in a petri dish is
approximated by the function G(t) = 500e 0.216t ,
where t is time, in minutes. Use this model to
approximate, to the nearest integer, the number of
bacteria present after one half-hour.
4
Algebra 2/Trigonometry Regents Exam 0117
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33 Given f(x) = x 2 and g(x) = x − 3, express
g(f(x + 2)) as a polynomial in simplest form.
2
 27  − 3
29 Determine the exact value of   as a fraction
 64 
in simplest form.
30 State the conjugate of 7 −
simplest a + bi form.
31 Express
34 Sketch an angle of 250° in standard position and
then express cos 250° as a cosine function of
a positive acute angle.
−48 expressed in
12x −5 y 5
in simplest form, using only
24x −3 y −2
positive exponents.
32 In a theater with 30 rows, the number of seats in a
row increases by two with each successive row.
The front row has 15 seats. Find the total seating
capacity of the theater.
35 Solve the inequality x 2 − 3x − 4 > 0 algebraically
for x.
36 The table below shows the minimum hourly wage, in U.S. dollars, for selected years since 1955.
Write the linear regression equation for this set of data, rounding all values to three decimal places. State the
strength and direction indicated by the correlation coefficient.
37 Solve the system of equations algebraically for x
y x−3
=
and y:
2
x
38 A rocket is shot vertically into the air. Its height, h,
at any time, t, in seconds, can be modeled by the
equation h = −16t 2 + 184t . Determine
algebraically, the number of seconds it will take the
rocket to reach a height of 529 feet.
y+2= x
39 Forces of 22 pounds and 43 pounds act on an
object at an angle of 52°. Determine, to the nearest
pound, the magnitude of the resultant force. Find,
to the nearest degree, the angle between the
smaller force and the resultant force.
5
ID: A
0117a2
Answer Section
1 ANS: 3
 π  17π
 =
510 

6
 180 
PTS: 2
REF: 011701a2
STA: A2.M.2
KEY: radians
2 ANS: 3
PTS: 2
REF: 011702a2
TOP: Analysis of Data
KEY: bias
3 ANS: 4
x 4 − 13x 2 + 36 = (x 2 − 4)(x 2 − 9) = (x − 2)(x + 2)(x − 3)(x + 3)
PTS: 2
REF: 011703a2
STA: A2.A.7
KEY: higher power
4 ANS: 2
y = (4) − 4 = 0
x 2 − 4(x − 4) 2 = 16
x 2 − 4(x 2 − 8x + 16) = 16
y=
x 2 − 4x 2 + 32x − 64 = 16
TOP: Radian Measure
STA: A2.S.2
TOP: Factoring Polynomials
 20 
  − 4 = 8
 3 
3
 
3x 2 − 32x + 80 = 0
(3x − 20)(x − 4) = 0
x = 4,
PTS:
KEY:
5 ANS:
TOP:
6 ANS:
x ±σ
20
3
2
REF: 011704a2
STA: A2.A.3
algebraically
1
PTS: 2
REF: 011705a2
Differentiating Permutations and Combinations
3
TOP: Quadratic-Linear Systems
STA: A2.S.9
62 ± 12
50 − 74
PTS: 2
KEY: interval
7 ANS: 2
3
2
1
2
REF: 011706a2
3
1
3
STA: A2.S.5
TOP: Normal Distributions
STA: A2.A.8
TOP: Negative and Fractional Exponents
9
2
2
2
 
9 • 27 =  3 2  2 • (3 3 ) = 3 3 • 3 = 3
 
PTS: 2
REF: 011707a2
1
ID: A
8 ANS: 3
1
2 60° 4
=
=
45° 3
Arc tan1
Arc cos
PTS: 2
REF: 011708a2
STA: A2.A.64
KEY: basic
9 ANS: 1
PTS: 2
REF: 011709a2
TOP: Sigma Notation
10 ANS: 1
k
1


6  3m 2 − k 3  = m 12 −
18 = 2m 3 − k 2
3
3


PTS: 2
REF: 011710a2
KEY: with variables | index = 2
11 ANS: 3
log 3 (x + 1) − log 3 x = 2
log 3
TOP: Using Inverse Trigonometric Functions
STA: A2.A.34
STA: A2.A.14
TOP: Operations with Radicals
STA: A2.A.28
TOP: Logarithmic Equations
REF: 011712a2
STA: A2.A.38
STA: A2.A.74
TOP: Using Trigonometry to Find Area
REF: 011714a2
STA: A2.A.46
REF: 011715a2
STA: A2.A.29
STA: A2.A.16
TOP: Addition and Subtraction of Rationals
x+1
=2
x
x+1
= 32
x
9x = x + 1
x=
PTS:
KEY:
12 ANS:
TOP:
13 ANS:
1
8
2
REF: 011711a2
applying properties of logarithms
4
PTS: 2
Defining Functions
2
A = 4 ⋅ 5 3 sin60 = 20 3 ⋅
3
= 30
2
PTS: 2
REF: 011713a2
KEY: parallelograms
14 ANS: 4
PTS: 2
TOP: Transformations with Functions
15 ANS: 4
PTS: 2
TOP: Sequences
16 ANS: 1
3
3
3
3
+
=
−
=0
a −1 1−a a −1 a −1
PTS: 2
REF: 011716a2
2
ID: A
17 ANS: 2



 2 2 + 5i   5 2 − 2i  = 10 4 − 4i



2 + 25i 2 − 10i 2 = 30 + 21i 2
PTS: 2
REF: 011717a2
18 ANS: 3
1
−b −(−7) 7 c −3
=
= .
=
= −
6
6
2
a
6 a
TOP: Operations with Complex Numbers
PTS:
KEY:
19 ANS:
TOP:
20 ANS:
21 ANS:
STA: A2.A.21
2
REF: 011718a2
basic
4
PTS: 2
Domain and Range
1
PTS: 2
1
TOP: Roots of Quadratics
REF: 011719a2
STA: A2.A.39
KEY: real domain, absolute value
REF: 011720a2
TOP: Graphing Exponential Functions
3
−
2
3
1
cos θ
1
•
=
= −2 3
. csc θ • cot θ =
If sin θ = and θ terminates in Quadrant II, cos θ = −
sin θ sin θ
2
2
 1  2
 
 2 
 
PTS: 2
22 ANS: 2
72
≠ 12
π
6⋅
180
REF: 011721a2
TOP: Determining Trigonometric Functions
PTS: 2
KEY: arc length
23 ANS: 1
6 P 4 = 360
REF: 011722a2
STA: A2.A.61
TOP: Arc Length
PTS: 2
24 ANS: 4
REF: 011723a2
STA: A2.S.10
TOP: Permutations
Michelle
Valerie
x
77.8
79
PTS: 2
REF: 011724a2
25 ANS: 4
17
sin −1
≈ 58.21° 0.21 ⋅ 60 = 12.6
20
PTS: 2
REF: 011725a2
σx
IQR
16.5
4
8.4
2.2
Range
20
6
TOP: Central Tendency and Dispersion
STA: A2.A.55
3
TOP: Trigonometric Ratios
ID: A
26 ANS: 1
 x + 2 
 − 2 = x + 2 − 2 = x
f  f −1 (x) = 3 
 3 
PTS: 2
REF: 011726a2
27 ANS: 4
PTS: 2
TOP: Inverse of Functions
28 ANS:
G(30) = 500e
0.216(30)
PTS: 2
29 ANS:
2
STA: A2.A.45
REF: 011727a2
KEY: graphs
TOP: Inverse of Functions
STA: A2.A.44
STA: A2.A.12
TOP: Evaluating Exponential Expressions
≈ 325,985
REF: 011728a2
2
−
2
 27  3  64  3  4 
  =   =   = 16
 64 
 27 
 3
9
 
 
 
PTS: 2
REF: 011729a2
STA: A2.N.1
TOP: Evaluating Expressions with Negative/Fractional Exponents
30 ANS:
7 + −48 = 7 + 4i 3
PTS: 2
31 ANS:
y7
REF: 011730a2
STA: A2.N.8
TOP: Conjugates of Complex Numbers
REF: 011731a2
STA: A2.A.9
TOP: Negative Exponents
2x 2
PTS: 2
32 ANS:
a n = 15 + 2(n − 1)
s 30 =
a 30 = 15 + 2(30 − 1) = 73
30(15 + 73)
= 1320
2
PTS: 2
REF: 011732a2
STA: A2.A.35
TOP: Series
33 ANS:
f(x + 2) = (x + 2) 2 = x 2 + 4x + 4 g(f(x + 2)) = x 2 + 4x + 4 − 3 = x 2 + 4x + 1
PTS: 2
KEY: variables
REF: 011733a2
STA: A2.A.42
4
TOP: Compositions of Functions
ID: A
34 ANS:
−cos 70°
PTS: 2
REF: 011734a2
STA: A2.A.57
TOP: Reference Angles
35 ANS:
x 2 − 3x − 4 > 0. x − 4 > 0 and x + 1 > 0 or x − 4 < 0 and x + 1 < 0
(x − 4)(x + 1) > 0
x > 4 and x > −1
x < 4 and x < −1
x>4
x < −1
PTS: 2
REF: 011735a2
STA: A2.A.4
KEY: one variable
36 ANS:
y = 0.098x + 0.402 high, positive correlation
TOP: Quadratic Inequalities
PTS: 4
REF: 011736a2
TOP: Regression
37 ANS:
x−2 x−3
y = 4 − 2 = 2 (4,2),(1,−1)
=
x
2
y = 1 − 2 = −1
x 2 − 3x = 2x − 4
KEY: linear
x 2 − 5x + 4 = 0
(x − 4)(x − 1) = 0
x = 4,1
PTS: 4
KEY: AII
38 ANS:
REF: 011737a2
16t 2 − 184t + 529 = 0 t =
184 ±
STA: A2.A.3
TOP: Other Systems
(−184) 2 − 4(16)(529) 184 + 0
=
≈ 5.75
2(16)
32
PTS: 4
REF: 011738a2
KEY: quadratic formula
STA: A2.A.25
5
TOP: Solving Quadratics
ID: A
39 ANS:
x=
22 2 + 43 2 − 2(22)(43) cos 128 ≈ 59
PTS: 6
REF: 011739a2
siny sin 128
=
59
43
 43 sin 128 
 ≈ 35
y = sin −1 

59


STA: A2.A.73
6
TOP: Vectors